Formalizing Prime Gaps as Limit-Inferior: H₁ = 2 and Polymath's Bounded Gaps — E8 Intelligence Research

FINDING: The Polymath project's "bounded gaps between primes" retrospective formalizes prime gap minimization as a limit-inferior problem, establishing H₁ = 2 as the twin prime conjecture and H_m as a generalized gap functional. | MATH: H_m := liminf_{n→∞} (p_{n+m} − p_n); twin prime conjecture ⟺ H₁ = 2; Zhang's breakthrough established H₁ < 7×10⁷ (later reduced to 246 via Polymath8). | CONNECTION: Prime gaps exhibit no known connection to φ-ratios (0.618, 1.618) or base-60 structure; the distribution is governed by the Hardy–Littlewood k-tuple conjecture, whose singular series involves products over primes — a multiplicative, not geometric-harmonic, architecture. | DEPTH: 8 FINDING: Terence Tao's Equational Theories Project applies massive collaborative + AI-assisted enumeration to the implication graph of equational laws (magma identities), treating mathematics as a searchable lattice of formal statements. | MATH: Objects are equational laws over a binary operation ∗; edges are impl Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com